I'm trying to manipulate mega2560 Timer5 in order to set phase and frequency correct pwm on pins 44 e 45 but I don't really know much about register and prescalers so I got 2 questions. I need to set a 10kHz frequency on that pins, am I able to change only OCR5A value to obtain 10kHz? Or there is a prescaler to set that helps me going much more near to desired frequency?

I'm trying to understand:
16MHz/10kHz= 1600
OCR5A=1600; //MEANS 10KhZ
DID I dream that?

16MHz/64...16....8...1/256
here is 16MHz/1/256= 62500 Hz pwms??

//arduino mega2560 Timer5 
//here is my code where I generate 799,92Hz freq, PWM of 
//75% on OC5B and PWM of 75% on OC5C with clock system
//phase & freq correct PWM

int outputB = 45; //D45
int outputC = 44; //D44

void setup()
{
//outputs via timer5
 pinMode(outputB, OUTPUT);  // select Pin as ch-B
 pinMode(outputC, OUTPUT);  // select Pin as ch-C
 
 TCCR5A = B00101001; // Phase and frequency correct PWM change at OCR5A
 TCCR5B = B10001;  // System clock
 OCR5A = 10000; // 799,92Hz
 OCR5B = 7500; // 75%
 OCR5C = 7500; // 75%
 }

Thank you for your help!

int outputB = 45;
int outputC = 44;

void setup()
{

 pinMode(outputB, OUTPUT);  // select Pin as ch-B
 pinMode(outputC, OUTPUT);  // select Pin as ch-C
 
 TCCR5A = B00101001; // Phase and frequency correct PWM change at OCR5A
 TCCR5B = B10001;  // System clock
 OCR5A = 1599; // 16MHz/10kHz=1600   prescaler set to 1
 OCR5B = 0; 
 OCR5C = 0;//motors stop
 }
 

What does it change between writing as I did and using _BV() | _BV() function to set bits HIGH?

On my google long trips I found that:

//...after ARDUINO UNO Timer1 (phase and freq correct) pwm settings
//20kHz

void setPWM(uint8_t pin, int dutyCycle) { // dutyCycle is a value between 0-TOP
  if(pin == leftPWM) {
    OCR1AH = (dutyCycle >> 8); 
    OCR1AL = (dutyCycle & 0xFF);
  } else if (pin == rightPWM) {
    OCR1BH = (dutyCycle >> 8);
    OCR1BL = (dutyCycle & 0xFF);    
  }
}

Why do we rewrite those bits?

Isn't required to access the 16 bit registers in the 8 bit processors?

The Timer/Counter (TCNTn), Output Compare Registers (OCRnA/B/C), and Input Capture Register (ICRn) are all
16-bit registers. Special procedures must be followed when accessing the 16-bit registers. These procedures are
described in the section "Accessing 16-bit Registers" on page 135.

The TCNTn, OCRnA/B/C, and ICRn are 16-bit registers that can be accessed by the AVR CPU via the 8-bit data
bus. The 16-bit register must be byte accessed using two read or write operations. Each 16-bit timer has a single 8-
bit register for temporary storing of the high byte of the 16-bit access. The same Temporary Register is shared
between all 16-bit registers within each 16-bit timer. Accessing the low byte triggers the 16-bit read or write operation.
When the low byte of a 16-bit register is written by the CPU, the high byte stored in the Temporary Register,
and the low byte written are both copied into the 16-bit register in the same clock cycle. When the low byte of a 16-
bit register is read by the CPU, the high byte of the 16-bit register is copied into the Temporary Register in the
same clock cycle as the low byte is read.

Not all 16-bit accesses uses the Temporary Register for the high byte. Reading the OCRnA/B/C 16-bit registers
does not involve using the Temporary Register.
To do a 16-bit write, the high byte must be written before the low byte. For a 16-bit read, the low byte must be read
before the high byte.

The AVR GCC compiler knows enough to write the high byte first and read the high byte second when doing a 16-bit operation on one of the 16-bit registers that has a shadow high byte TEMP register.